Go to the southeast exit grid in the Downtown section of the Hub. Enter the building toward the west in the following area, and go into the back office. Once inside the office, kill the woman in purple robes. Be warned, once Jain dies, everyone else in the building will go hostile with the Vault Dweller.
If the Vault Dweller has an Intelligence of 1, completing this quest becomes nigh-impossible; if the Vault Dweller has an Intelligence of at least 2 (maximum 4), Mentats will be needed to take the quest.